A Numerical Proof of Shell Model Turbulence Closure
This work addresses the theoretical challenge of turbulence closure for fluid dynamics, with potential applications in fields like weather prediction and engineering, though it is incremental as it builds on existing methods in a specific domain.
The authors tackled the challenge of turbulence closure models by developing a deep recurrent neural network closure that quantitatively reproduces Eulerian and Lagrangian structure functions and intermittent statistics within statistical errors, using shell models of turbulence to achieve high-order statistical accuracy.
The development of turbulence closure models, parametrizing the influence of small non-resolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance. We present a closure, based on deep recurrent neural networks, that quantitatively reproduces, within statistical errors, Eulerian and Lagrangian structure functions and the intermittent statistics of the energy cascade, including those of subgrid fluxes. To achieve high-order statistical accuracy, and thus a stringent statistical test, we employ shell models of turbulence. Our results encourage the development of similar approaches for 3D Navier-Stokes turbulence.